基于自然指数模型的机床定位误差建模与实时补偿

摘要

This paper proposes a novel modeling method based on natural exponential model to improve the positioning accuracy of CNC machine tools.Through the analysis of positioning error measurement data under different temperature conditions,the positioning error can be divided into two terms:geometric and thermal term.A polynomial can be used to establish the relationship between the geometric term and the position coordinate.A natural exponential model can be used to establish the non-linear relationship between the thermal term,the ambient temperature,and the temperature of the key machine component.The experimental results show that the proposed model performs better than the traditional multiple linear regression model in terms of prediction accuracy under different temperature conditions,which can be applied to the error compensation so as to improve the machine tool accuracy.%为提高数控机床的运动性能和加工精度,提出了基于自然指数模型的机床定位误差建模方法.通过分析在不同温度条件下的定位误差变化规律,将定位误差分为几何误差和热误差两个部分,其中,几何误差部分可以采用多项式模型进行拟合,而对于热误差部分,则建立其与环境温度、机床关键构件温度之间的自然指数模型,从而描述了热误差和温度场之间的非线性变化规律.通过与传统的多元线性回归模型进行试验结果对比表明:基于自然指数模型的定位误差建模方法在任何温度条件下均可获得较高的预测精度,经过误差补偿,可以大幅提高机床精度.